Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26021937 | C2 | semidirect |
| 2. #26021917 | C2 | semidirect |
| 3. #26018412 | C2 | semidirect |
| 4. #26018409 | C2 | semidirect |
| 14. #532×C89 | C4 | semidirect |
| 17. #497×C89 | C4 | semidirect |
| 20. #496×C89 | C4 | semidirect |
| 22. C2×#97×C89 | C4 | semidirect |
| 178. C89 | #13577 | semidirect |
| 181. #532 | Dic89 | semidirect |
| 184. #497 | Dic89 | semidirect |
| 187. #496 | Dic89 | semidirect |
| 191. C2×#97 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021937 | 2 |
| #26021917 | 2 |
| #26018412 | 2 |
| #26018409 | 2 |
| C89×#3150 | 2 |
| #13577 | 89 |